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SOME REVIEW QUESTIONS: Chapter 9
1) Four different statistics are being considered for estimating a population characteristic. The sampling
distributions of the four statistics are shown here. Which statistic is most likely to result in an estimate
that is close to the true value of the population characteristic?
2) To estimate the proportion of students at a university who drive SUVs, a random sample of 100
students was selected and resulted in a sample proportion of 0.24. A 90% confidence interval for the
true proportion of students at the university who drive an SUV would be _______ a 95% confidence
interval.
a) narrower than
b) the same width as
wider than
3) Suppose that a random sample of 100 students at a university is selected and a 95% confidence
interval for the proportion that drives SUVs is (0.16, 0.32). Which of the following is a correct
interpretation of the 95% confidence interval?
a. We are 95% confident that the sample proportion is between 0.16 and 0.32.
b. The method used to construct the interval will produce an interval that includes the value of the
sample proportion about 95% of the time in repeated sampling.
c. There is a 95% chance that the true proportion of students at this university that drive SUVs is
between 0.16 and 0.32.
d. We are 95% confident that the true proportion of students at this university that drive SUVs is
between 0.16 and 0.32.
4) Suppose that a random sample of 100 students at a university is selected and a 95% confidence
interval for the proportion that drive SUVs is (0.16, 0.32). Which of the following is a correct
interpretation of the 95% confidence level?
a. We are 95% confident that the sample proportion is between 0.16 and 0.32.
b. The method used to construct the interval will produce an interval that includes the value of the
population proportion about 95% of the time in repeated sampling.
c. There is a 95% chance that the true proportion of students at this university that drive SUVs is
between 0.16 and 0.32.
d. We are 95% confident that the true proportion of students at this sample that drive SUVs is between
0.16 and 0.32.
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5) Assuming that the sample proportion remains unchanged, the width of the confidence interval for a
population proportion ______ as the sample size increases.
a) decreases
b) increases
c) stays the same
6) When determining the sample size necessary to estimate a population proportion π to within an
amount B with 95% confidence, in the absence of any knowledge about the value of π, using π = _____
will give a conservatively large value for the required sample size.
a) 0.1
b) 0.2
c) 0.3
d) 0.4
e) 0.5
7) Which of the following assumptions must be true of a sample to use a t confidence interval to
estimate the population mean?
a) The sample is a random sample from the population of interest.
b) n∙p≥ 10 and n∙(1-p) >= 10
c) The population distribution is normal or the sample size is large.
d) All of the above are required assumptions to use the t confidence interval to estimate the population
mean.
e) Only choices a and c are required assumptions to use the t confidence interval to estimate the
population mean.
8) Each individual in a random sample of 60 college students was asked how many times he/she ate at
the student union for lunch in a typical month. The data was then used to construct a 90% confidence
interval for the true mean number of times all students at the college ate lunch at the union in a typical
month. The confidence interval was (10.5, 19.5). Which of the following could be the 95% confidence
interval constructed using the same sample data?
a) (11.2, 18.8)
b) (9.8, 20.2)
c) (8.8, 19.8)
d) none of these
9) The Bureau of Alcohol, Tobacco and Firearms (ATF) has been concerned about lead levels in California
wine since the 1980s. In a recent ATF study, the agency measured lead content (in parts per million) in
100 randomly selected bottles of California wine. The resulting 90% confidence interval was (69.91,
75.36). Which of the following is a correct interpretation of the confidence interval?
a) There is a 90% chance that the mean lead content of all California wines is between 69.91 and 75.36.
b) We are 90% confident that the sample mean is between 69.91 and 75.36.
c) We are 90% confident that the mean lead content of all bottles of California wine is between 69.91
and 75.36.
d) 90% of all bottles of California wine will have a lead content between 69.91 and 75.36.
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10) One hundred holders of a particular credit card were selected at random and each was asked
whether or not they pay off their credit card in full each month. Assuming that the sample size is large
enough, which of the following confidence intervals should be used to estimate the fraction of all holders
of this credit card who pay off their balance each month?
a)
b)
c)
d)
none of these
11) One hundred holders of a particular credit card were selected at random and each was asked the
balance on their card at the end of the previous month. Assuming that the sample size is large enough,
which of the following confidence intervals should be used to estimate the average balance at the end of
the previous month of all holders of this credit card?
a)
b)
c)
d)
none of these